For a given \(k\) , \(F_n\le k \le F_{n+1}\) . From proposition \(2.7\)  in [1]}, the first occurrences of \(k+1\)  distinct factors of length \(k\)  are given by
\(v_j= {\left\lbrace \begin{array}{ll}f[j;~k] & \text{if~~}1\le j \le F_n \\f[j+F_{n+1}-(k+1);~k] & \text{if~~} F_n+1\le j\le k+1\end{array}\right.} \) 
